9-4 Law of Sines

Law of Sines is be only used when solving non-right triangles. There will be but 2 answers for the inverse. It is can be used when u know an angle and an opposite.

The formula is

sinA/a=sinB/b=sinC/c

To solve all that needs to be done is cross-multiplication

Ex 1:

Triangle ABC angle A= 110 degrees angle C= 50 degrees Side c=25m

Solve the triangle:

Interior angles add up to 180 degrees in a triangle so add up 110 and 50 then subtract the sum from 180 to find angle B.

Angle B= 20 degrees

To find side a apply law of Sines.

sin 50 degrees (C)/25 m=sin 110 (A)/ side (a)

Cross multiply and you'll get 25 sin110=sin 50

So plug in 25 sin 110 and you'll get 23.492

So set that equal to sin 50 degrees

It should look like 23.492=sin 50

Divide sin 50 degrees on both sides

side (a)= 14.837m

To find side b apply law of Sines

b= sin 50 degrees(C)/25 m=sin 20/side(b)

Cross multiply again and you'll get 25 sin 20=sin 50 degrees

Divide both sides by sin 50 degrees

The answer comes out to be 11.162 m=side b

-Sameer